introduction: silence and sound
TRANSCRIPT
ÚSTAV HUDEBNÍ VĚDY, FILOZOFICKÁ FAKULTA, MASARYKOVA UNIVERZITA V BRNĚ
MARTIN CELHOFFER
MAGISTERSKÁ DIPLOMOVÁ PRÁCE
SILENCE AND SOUND: ESSAYS ON THE ONTOLOGY OF MUSIC
Vedoucí práce: doc. PhDr. Lubomír Spurný, Ph.D.
Konzultant: Dr Elizabeth Eva Leach
BRNO 2006
Prohlašuji, že jsem pracoval samostatně, s použitím uvedené literatury.
Martin Celhoffer
V Brně, dne 19. června 2006
Summary
This writing deals with one of the most problematic issues in musicology - the
ontology of music. The themes selected are developed on the background of antinomy
between sound and silence. This antinomy was understood as (i) audible and inaudible
categories of music during Antiquity and Middle Ages; (ii) object (sound-concepts, sound-
structures) and subjective condition (‘silence’ of a priori givenness of perceptual and
cognitional faculties of a man) during the modern era. Chapters are organized chronologically
showing the evolution of the idea of world harmony from Antiquity till the early empirics in
the first part; and the theories of modern philosophical concern in metaphysics of music in the
second part. The study also reflects how music was apprehended methodologically: as (i) a
multidisciplinary field incorporating music, mathematics, astronomy, astrology; (ii) a
philosophy of music integrating epistemology and ontology.
Práce je věnována snad nejdiskutabilnější otázce muzikologie - ontologii hudby.
Vybrané tematické okruhy jsou rozvíjeny ve světle základního protikladu mezi zvukem a
tichem. Tento protiklad je pojímán jako (i) otázka kategorizace hudby na ‘slyšitelnou’ a
‘neslyšitelnou’ v období antiky a středověku; (ii) otázka vztahu objekt (zvukový koncept nebo
struktura) a subjekt (‘ticho’ apriorních daností lidského vnímání a umu) v období novověku.
Jednotlivé kapitoly jsou řazeny chronologicky, v první části práce vypovídají o vývoji
myšlenky ‘harmonie kosmu’ od antiky až po raný empirismus; ve druhé části o různých
novověkých filozofických teoriích zabývajících se metafyzikou hudby. Práce také odráží jak
byla ontologie hudby chápána z metodologického hlediska: jako (i) multidisciplinární přístup
zahrnující hudbu, matematiku, astronomii a astrologii; (ii) filozofie hudby zahrnující
epistemologii a ontologii.
Contents
PREFACE.............................................................................................................................................................. 1
INTRODUCTION: SILENCE AND SOUND .................................................................................................... 3
PART ONE: THE COSMOLOGY OF MUSIC................................................................................................. 9
Pythagorean tetractys ........................................................................................................... 10
Plato’s World-Soul ............................................................................................................... 16
Boethius’ Musica Mundana ................................................................................................. 21
Kepler’s Planetary Polyphony.............................................................................................. 26
PART TWO: POST-COSMOLOGICAL CONCEPTIONS ........................................................................... 31
Immanuel Kant: Mind as a ‘string instrument’ .................................................................... 33
Schopenhauer: Music as representation of the Will............................................................. 40
Phenomenology and ontology of Music............................................................................... 46
CONCLUSION.................................................................................................................................................... 52
BIBLIOGRAPHY ............................................................................................................................................... 56
Preface
The aim of this paper is to interpret some of the basic assumptions of evaluation the
ontological status of music. This issue never stood alone among the other disciplines, but
became an indispensable part of our interpretations of all phenomena, whether related to
music directly or not. When I had asked myself the question why is the ontology so
fascinating and important for musicology, the well-known Schopenhauer’s statement arose in
my mind:
For in every mind which once gives itself up to the purely objective
contemplation of the world, a desire has been awakened, however concealed and
unconscious, to comprehend the true nature of things, of life, and of existence.
(Schopenhauer, 1958, p.406)
This ‘concealed desire’ is a prime mover of our investigation. The fact that satisfactory
answer to the questions concerning ‘true nature of things’, particularly the ontology of music,
could not be provided does not make the attempt of this writing quixotic. The questions are
not to be answered, simply because there is no answer to comprehend all the dimensions of
real world in one individual theory.
As I propose later, examining the ontology of music is not considered as independent
and integrated theory, but might provide us with understanding of basic premises for various
consecutive theories. A causa de cy the approach I have chosen quadrates with series of
essays of individual subjects. The essays are organized chronologically and are arranged into
the two parts: (1) The cosmology of music and (2) Post-cosmological conceptions. The
cosmology of music is a gradually developing concept with common axioms. On the contrary,
post-cosmology consists of various, occasionally contradictory theories, refusing the axiom-
wise heritage of Antiquity and Middle ages.
The common thread implicitly running across this writing is the idea exposed by the
title: the antinomy between the terms ‘silence’ and ‘sound’. The emphasis of this antinomy is
given in the introduction. The reason for such a literary and not ‘scientific’ title I found in
fact, that audibility and inaudibility of music was one of the key issues in cosmology in
accordance to ontology. On the other hand, the theories of post-cosmology deal with sound in
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terms of sound-constructs or sound structures of musical work, and with silence in terms of
subjective and general conditions, the question of audibility and inaudibility no more holds
sway.
I have omitted extensive throng of philosophers and music theorists that have
contributed to reception of the ontological issue of music. I did not intend to present a
comprehensive enumeration of theorists, but I have pursued the tracks of some important
tendencies.
Last but not least, I would like to express my thanks going to supervisors of this
writing, Dr Elizabeth Eva Leach and doc. PhDr. Lubomír Spurný, Ph.D., who have given so
generously of their time in granting so many advises and guidance upon my work.
2
Introduction: Silence and Sound
‘It is silence here’, statements like this or similar are used to describe a particular state
of exchanging information between subject and environment. The semantic context of this
utterance may differ: a suspicious silence, a pleasant silence, or an embarrassing silence. In
fact, ‘silence’ means ‘relative silence’ as there is ultra-sound and infra-sound lying beyond the
grasp of man ear. On the contrary, sound itself is conditional on a complicated process of
perception. Thus silence and sound could be considered vice-versa: sound as silence and
silence as sound. Consequently, the dichotomy of hearing is accepted as relative. While
silence has always the same quality in terms of acoustics, sound has many forms and patterns
sometimes evading from hearing. We built our ‘realm of sound’ on the basis of contingent
perceptual options.
As a subject transforms environmental forces into sophisticated perception, this might
be considered as disruption of subject’s equilibrium resulting generation of information. This
act is made through differentia, a kind of ‘mirrored’ activity whereabouts conditions below
the axis of disturbance are reflecting their nature above. Thus silence and sound refer to actual
process rather than to particular phenomenon as an object by itself. Accounts of this, absolute
silence and absolute sound are abstract theoretical notions.
Silence and sound are not being further set out from acoustical point of view as might
have been expected. The approach to these categories by means of philosophical speculation
may uncover basic facets of our assumptions for understanding music. In addition, ‘silence
and sound’ hint at dynamical dichotomy of inherency, particularly in music. Music arises
from a dialogue between them, from their interaction. Does music tacitly mean peculiar
paradigm of sound otherwise can music be in specific case silent? This issue occurs when
approaching to Pythagoras, Plato, Boethius and many other theorists.
It is possible to imagine many things by the term music: a well-known melody, a
popular hit, soundtrack, musical, opera, a village song or a great symphonic work. We hardly
ever imagine something else quite different from the notion of sounding structure. Our
understanding of music is exclusively perceptual. However, for Pythagoreans the term music
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means mathematics. Music was for them a science par excellence, a science providing the key
for understanding the cosmos, a universal harmony holding and uniting everything. These two
conceptions, one based on perceptual quality and another pointing out its ontology, represent
perceptual and meta-perceptual paradigm of understanding the term music.
Music is unpromptedly associated with an act of hearing. Thus the purpose of music
was described as ‘to delight the human ear’ in many treatises, emphasizing the aspect of
aesthetic perception. However, music was also considered as ‘a science’ dealing with act of
understanding and meta-sensual experience. Another conception is that of the Memoria:
music can be stored in human memory and contrariwise restored from it. Moreover, on the
mediaeval concept of memory is based the creative ability - inventio (Ziolkowski 2002,
p.297).
The relations of these antimonies discussed thus far are presented in table 1. The
horizontal axis ‘x’ describes the perceptual and meta-perceptual dichotomy. The vertical axis
‘y’ divides the bilateral phenomena of sound and silence. Music is described as a set
containing determinate areas of every category involved.
Table 1.
If we are trying to understand what the word music actually means, it would be
unavoidable to establish an ontological dispute. In a general way, what is the nature of any
given real particularity? ‘The nature of something’ in terms of ontology refers to quality not to
quantity and therefore is immeasurable. Therefore is not possible to define the word music as
the succession of coded pitches in spatial and temporal organization. Anyway, how should the
4
ontology of music then be construed? As we come to a resolution that music can be
considered as an ontological entity there is an intrinsic difference between treating this entity
as an object or as a homologue (Wallin, 1991) between the two or more objects. Namely the
term ‘object’ associates a natural entity with spatial and temporal organization that is possible
to perceive through the senses. On the contrary, a homologue means a correspondence which
can be to some extent abstract as well as measurable, for instance through mathematical
equation. Therefore, music is accepted as a multiple set of heterogeneous phenomena. In
order to investigate the ontology the examination is focused to the correlations among them.
Was this issue a crucial task for theorists during the antiquity and Middle Ages and
how was it aproached? Quid est Musica? - appears in various Latin writings on music usually
at the very beginning of treatise. The answer mostly refers to the reinterpretation of Greek
thought that portrays music as an activity of the Muses or as a reflection of cosmic harmony
or harmony by itself ruled by Creator - a supreme being. But the ontology of music eo ipso,
as a discrete discipline, was never a principal and outstanding issue for such philosophers as
Pythagoras, Plato, Plotinus or Boethius. In this sense the ontology of music had an
interpretative quality of evaluating the aesthetic potential of music or like a ‘theory of
everything’ - integrating axiom of all phenomena.
It is possible to provide a satisfactory answer to the question of what music is? Why is
this question considered irrelevant in musicology and beside the point of science? The
ultimate limit for acceptability of knowledge is given not explicitly by verification but in a
certain extent by operative paradigm in terms of common convention. Probably the whole of
knowledge has an abstract nature in the sense of projecting subjective notions onto reality. For
instance, a cube with scaling of 2 x 2 x 2 units represents a three-dimensional object of
cubage 8 units. This knowledge is mediated by empirical experience can be verified and
simply imagined. But mathematicians are already manipulating with more than three-
dimensional objects at the present time. That is to say, knowledge could be drawn from each
empirical experience, and applied consequently to the field where is no direct verification
based on classical empirics. The knowledge is not measurable by itself but through empiric
(table 2):
5
Table 2.
Empiricism provides a limited sum of verified data whereupon theories are construed.
Consequently, these theories are supposed to confer a noticeable order to the particular data.
In certain circumstances might the specific theory explain phenomena which are not possible
to verify empirically. For example, the ‘string field theory’ in physic is ‘verified’ by
mathematics and not by experiment. On the other hand, an empirically verified theory may
fail analogous to thermodynamics. This reflection is not being an attempt to contest with
verification in science but points out the very thin line disentangling acceptable and non-
acceptable theories. Thus satisfactory resolution of the issue in terms of utter definition seems
to be a quixotic investigation.
Music is the discipline that undoubtedly has an empirical base when focusing on the
angle of sound structure. But this positive facet might detract the understanding of its nature.
It is not surprising that in the modern era, whenever emphasis on empiricism in terms of a
touchstone is generally accentuated, it is currently the art most difficult to define in spite of its
material substance. By contrast, mathematics even though dealing mostly with abstract
numbers and theoretical dimensions eventually not possible to imagine is considered to be the
positive science. On what matter of fact rests this paradox? It is certainly not due to music
itself, i.e. to its acoustical structure and nature, but to the fact that music includes the
perception and understanding of a man’s subjectivity. Volker Kalisch states:
...if we speak about music we automatically have to deal with humans, with
human conditions, with ourselves. And vice versa: when we start to reflect upon the
nature of man we automatically reach a point where music intervenes. Being human
and experiencing music are clearly inseparable. (Kalisch, 2000, p. 309)
Therefore, music does not exclusively rest in sound and at least one facet of it is non-
empirical. On the proviso that music includes specific human perception and understanding, it
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will be necessary to deal with these phenomena. According to Cooke (1957, p.5), music is a
‘language of sub-consciousness’. Both terms are problematic alone and even more in their
juncture. It is a literary explanation, a sophisticated metaphor and therefore it should not be
taken au pied de la lettre. Simplistically said, a language is just a tool mediating particular
semantic notions. Its syntax can be understood by music theory and acoustics. It is not
necessary to emphasize how useful this would be in terms of musical analysis. But
investigation like this cannot shed a light to the nature of music. On the other hand, inclusion
of the assumption of subconsciousness’ existence seems to contribute to our ontological
dispute. This refers on basic antimony of this discourse: sound as a conscious phenomenon,
and silence as an unconscious phenomenon. From this point of view, Musica humana can be
interpreted as ‘subconscious music’ - ‘inaudible consonances’ of human mind subordinated to
higher quality of Musica mundana.
However, the nature of subconsciousness - or whatever we call it - is to a particular
extent an immeasurable part of the realm of our existence impenetrable with actual
measurements but perhaps penetrable with imagination, inspiration and contemplation.
Notably in the arts, imagination and inspiration have a crucial role and there are indispensable
parts of both creative and perceptive processes. If these qualities of subconsciousness
participate on music it might be the reason for exclusivity of phenomena such as aesthetics in
terms of unaccountability of its nature. Does it mean that these phenomena considering being
beyond actual methodological grasp are less important?
As it can be seen from previous allusive explanations, an approach to the ontology of
music can be pursued from various directions. However, the basic intention of them is to
supply a background for interpretation of cosmology of music. A number of key notions
(Pythagorean tetractys, Plato’s World-Soul, Boethius’ Musica Mundana, and Kepelr’s
Planetary polyphony) ranked chronologically will be presented as representation of particular
conception of ontology. A common thread of these conceptions is the idea of cosmology and
how this was reinterpreted in antiquity, Middle Ages, and Renaissance. The structure of study
was deliberately set up on a number of essays and therefore it is not intended as a
comprehensive study on ontology of music. I tried to avoid generalizations and
simplifications although more extensive historical background would be desirable for
advanced and more accurate research. Intention of examining ontological issues is to provide
paradigms for understanding music, for drawing courageous parallels between the past and
present. Aspiration of this study is not in presenting the notion of ontology as a scientific
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method but as a cognitive-literary dialogue between mind and imagination, the reason and the
art, and between silence and sound.
8
PART ONE: THE COSMOLOGY OF MUSIC
The cosmology of music is an interdisciplinary achievement bringing together
mathematics, astronomy (eventually astrology), and music. Although the first essay is devoted
to Pythagorean doctrine of tetractys, we should bear in mind that the formal sources of
Pythagoreans are running back to Babylonians (McClain, 1984). The cosmology presupposes
a series of common premises, which were gradually shifted in pursuance of new empirical
data. This progression is recorded in four following essays, from Pythagorean tetractys to the
theory of Kepler’s ‘harmony of the world’.
The hypotheses about the cosmology of music were set out on the basis of
contemporary understanding of the universe. Neugebauer (1969, p.171) noted that:
To a modern scientist, an ancient astrological treatise appears as mere
nonsense. But we should not forget that we must evaluate such doctrines against the
contemporary background. To Greek philosophers and astronomers the universe was a
well defined structure of directly related bodies. The concept of predictable influence
between these bodies is in principle not at all different from any modern mechanistic
theory.
However, the Greek view on cosmos drew its formal conception either from
mythology. It was generally accepted that the universe was settled by mythical beings. And
celestial music was their expression. Forasmuch as the empirical data were missing in
Antiquity and Middle Ages, and therefore there was no physical conception of sound, the
antinomy of silence and sound – the audibility and inaudibility of this music varied among
authors. The theory of musical cosmology was, in fact, an attempt to discover ‘the theory of
everything’ - the universal knowledge conferring the sense to all phenomena. Sound was
metaphorically confused with immaterial harmonious order of random phenomena.
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Pythagorean tetractys
The essence of all things rests in numbers - this was a rudimental premise for
Pythagoreans. A notion of everything penetrating immaterial numeric principle was holding
sway among the Pythagoreans for nearly the whole millennium. Pythagoreans considered
music as the most reputable discipline due to its possibilities of discovering the numerical
ratios and verifying their hierarchy. However, this theorem of multilateral correlation between
the number and music was also noted by Babylonians and Egyptians probably about two
thousand years or even more before Pythagoras (McClain, 1984). This suggests that
Pythagoras (c.560 - c.480 BC) was not inventor of this knowledge, but rather its importer to
Greece, and hints on his possible scholarship in Middle East. Though Lippman (1963) holds
the view, that ‘as difficult as it is to specify the older constituents of Pythagorean thought, it is
still more difficult to determine the precise achievements of Pythagoras himself’. This is even
complicated by the fact that of no authentic writing of Pythagoras has been preserved.
Therefore, the investigation and evaluation of Pythagoras’ own contribution is thrown upon a
number of secondary sources, which were written by his followers and other philosophers.
Pythagorean thoughts were transmitted to Christian mystics thanks to Plato’s (c.429 -
347 BC) writings, especially his Republic. Also Aristotle (384 - 322 BC) mentions some of
Pythagorean’s ideas in Methaphysics. Euclid (c.325 - 256 BC) presented the theory of
numerical ratios in Elements, books 7-9 based on Pythagorean music theory. Also
Nicomachus (c.60 - c.120 AD) discussed Pythagorean ratios in his Introductio arithmetica.
Ptolemy (c.90 - c.168) in his Harmonics - a summary of Greek knowledge on music, points
out Pythagoras’ contribution in terms of noting that music is the direct link ‘between the
microcosm and the macrocosm, between man’s soul and the universe’ (Gamwell, 2004). The
idea of the music of the spheres and codification of the regular proportional relationships
between particular tonal pitches is also generally accredited to Pythagoras (Harap, 1938;
Kinkeldey, 1948). Nevertheless, several myths about Pythagoras’ life emerged inevitably and
became legends. Unarguably, the most famous legend is the ‘hammer story’ found in
Nicomachus’ Manual of Harmonics and in many other writings. Another myth considers
10
Pythagoras as the inventor of monochord, but according to Waerden (1943) and Dykast
(2004), monochord emerged as late as in the third century BC.
Generally, Greeks imagined the earth as a flat disc confined by the river Oceanus
while Gods lived at the top of the mountain Olympus. The stars were assumed to be orbiting
around the earth. Ever since the notion of their trajectories being determined by certain
relations emerged, the particular celestial bodies were associated with particular spheres. It
was believed that a Siren was sitting on each sphere, or respectively, each sphere was ruled by
an individual deity. To how many spheres was the Pythagorean cosmos understood to be
divided is disputable. Meyer-Baer (1970, p.44) suggests an interesting hypothesis on a
possible view on cosmos:
In the south of Italy, a number of bronze vortices, or spindles, have been
found which consist of eight disc on an axis, their circumferences forming a kind of
double cone. It is probable that these, like the golden tablets found in the same area,
were used in the rites of the Pythagoreans, a sect which had several centers in southern
Italy and Sicily. Although the details of these rites have remained a secret, it is known
that the idea of the cosmos constructed in eight layers was a basic dogma of
Pythagorean belief. The image of the seven or eight spheres was derived from the
Babylonians, but the Pythagoreans added a new concept of numbers as a ruling
principle of the cosmos and also identified them with musical intervals.
However, no source seems to illustrate in greater detail, how is the mechanism of
spheres in ‘Pythagorean cosmos’ understood in terms of arithmos. Forasmuch, due to the lack
of sufficient and attested data in the ancient astronomy, the organization of the universe was
believed to follow the same rules as the organization of material in music, where the actual
measurements confirm the conception of arithmos and harmonia. Pythagoreans assumed all
things to be originated in numbers, and this axiom was applied to the ontology of all
phenomena. Thus music was a key, a gateway to a higher understanding – a ‘theory of
everything’.
Pythagoreans proposed a distinction between the notions of unity - immaterial being,
and multeity - material being. This basic antimony constitutes an ontological differentia,
which results in the act of creation:
...material world, being a physical entity, must have a limit. This limit is
inherent in the numbers 1, 2, 3, 4. They create the point, the line, the plane and the
volume. Adding up these dimensions, 1 + 2 + 3 + 4 = 10, we exhaust the limits of
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physical extension. There is no number following 10 that is not incapsulated in the
tetrad. Nothing can be added that does not exist as a combination of these four
numbers. Tetrad and decad are therefore the models of perfection. They create unity
out of multeity, and multeity out of unity. They originated in the unlimited, absolute
world, but when they extend into the physical world, they create a limited, yet perfect,
unified system, a universe. (Berghaus, 1992, p.45)
This very accurate interpretation of the tetractyl, i.e. a set of four numbers regarded as
the source of all things, suggests the basic constituents of Pythagorean thought. The dynamic
aspect of tetractyl and emergence of time quality is described as follows:
Time, or the fourth dimension, enters when the idea of number is given
physical extension. Chronological time (chronos) proceeds from eternity (aion), just
as finite space proceeds from infinity. The metaphor for this process is creation. The
act of creation establishes the monad in time and space. Time is a corollary product of
the creation of the physical world, and it prevents the created universe from remaining
static. The cosmos is dynamic, ever-changing. However, this constant motion is
ordered. The dimension of temporality is structured just like the spatial world. The
patterns of movement obey a scheme. All changes are phases proportionate
propensities. (Berghaus, 1992, p.45)
The Pythagorean conception of the genesis of universe shifted the traditional Greek
world-view and also the role of deity to a great extent. However, the only touchstone available
for experimental support of this doctrine was through music, especially the specification of
numeric ratios in musical intervals. There are two basic categories of ratios: superparticular,
defined by formula ; and reciprocal . With regard to this formulas,
superparticular ratios are 2:1, 3:2, 4:3 etc.; reciprocal 1:2, 2:3, 3:4 etc. These ratios are
equivocal according to string length (or cubage of air column) and frequency. Where
superparticular ratios determine the frequency, the reciprocal determine the string length and
vice versa:
diapason diapente diatessaron
string length 1:2 2:3 3:4
frequency 2:1 3:2 4:3
Table 3.
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This table represents the first three harmonics. Naturally, as the ratio sequence
continues further, frequency increases and, respectively, string length decreases. But only first
three ratios are considered as the perfect consonants. This is mathematically proven by the
fact that these ratios of ‘tetractycal’ numbers exclusively. Moreover, tetractys (1, 2, 3, 4 /
1+2+3+4=10) is a ground for basic numbers that constitute the ratios of consonances in
whichever combination: 4:1= double-octave, 3:1= octave + fifth, 2:1 or 4:2= octave, 4:3=
fourth, 3:2= fifth (addition of fifth and fourth results the octave and difference between them
the whole tone 9:8). The fact that what is sensually perceived as consonant and plausible
harmonious sounds can be expressed mathematically, suggests the hypothesis that everything
has its base in numbers. For all of the above, mathematics became the most reliable method of
codifying the rules of music and, consequently, the rules determining all phenomena.
Providing that the whole universe originates in number, multeity of all things is
unified by basic numerical patterns. Of course, this includes individual human beings: a body
and a soul. It is assumed, that Pythagoras believed that listening to the music has a specific
effect on the soul. The dynamic process in music evokes the congeneric process in the human
soul. Censorinus (early third century AD), a neopythagorean, states that music has a similar
effect on the soul as the stars. Similarly as music, astrology was understood to be determined
by numbers and geometrical figures (De die natali, XI-XIII, ed. O. Jahn, Berlin, 1845. IN:
Godwin, 1986, 19). Iambichus (c.250 - c.325 AD) points out ‘that music contributed greatly
to health, if it was used in an appropriate manner’ (Life of Pythagoras, translated by Thomas
Taylor, London, 1818, pp. 43-8, 80-3., IN: Godwin, 1986, p.28):
And there are certain melodies devised as remedies against the passions of the
soul, and also against despondency and lamentation, which Pythagoras invented as
things that afford the greatest assistance in these maladies. And again, he employed
other melodies against rage and anger, and against every aberration of the soul. There
is also another kind of modulation invented as a remedy against desires. He likewise
used dancing; but employed the lyre as an instrument for this purpose.
Therefore, the instrumental and vocal imitation of the music of the spheres was
considered as the ‘early music therapy’ (particularly in terms of mental health), through which
the harmonia between body and soul and between soul and cosmos was achieved. Censorinus
(Godwin, 1986) mentions that Pythagoras himself might have been used to play his lyre
before sleep and upon waking up ‘to imbue his soul with its divine quality’.
13
Another disputable issue emerges in connection with audibility of music of the
spheres. Various sources refer to the myth of Pythagoras’ exceptional ability to hear ‘celestial
harmony’. However, there are two quite different suggestions, and both can be found in
Simplicius’ (fl. first half of 6th c.) commentary on Aristotle’s On the Heavens (trans. by Th.
Taylor in The Theoretic Arithmetic of the Pythagoreans, London, 1816, IN: Godwin, 1986,
p.51):
Pythagoras, who is reported to have heard this harmony, should have his
terrestrial body exempt from him, and his luminous and celestial vehicle, and the
senses which it contains, purified, either through a good allotment, or through probity
of life, or through a perfection arising from sacred operations, such a one will perceive
things invisible to others, and will hear things inaudible by others.
Though Simplicius is quite skeptical about this possibly influenced by Platonic view
on disputable materiality of spheres. He assumed that if any sound emerges from superlunary
spheres (i.e. those of immaterial celestial bodies), it should be neither ‘percussive nor
destructive’ but it activates the ‘powers and energies’ of sublunary sounds (i.e. material), and
also affects the senses in terms of harmonization. Accordingly, there are the two types of
sound in the Pythagorean theory: material and immaterial. ‘If then, sound is not passive there
[i.e. in superlunary spheres] it is evident that neither will the sound which is there be passive’.
However, Simplicius suggested yet another view: he mentions that Pythagoras might have
said that he hears the harmony of the spheres as ‘understanding the harmonic proportions in
numbers, of the heavenly bodies, and that which is audible in them’.
The proportions which constitute human beings are homologous to proportions of the
universe, nature and music. The Pythagorean theory, leastwise as comes to us, incorporates an
ontological issue. From this point of view it was not only descriptive analysis of music, but
searching for ‘primordial principle’ that ‘extends into the material world and becomes
multeity’ (Berghaus, 1992, p.45). The musical sound is considered as an audible
representation of this principle. On the other hand, ‘ontological immaterial music’ rests in
number in the state of rest and becomes audible through the dynamics of tetractys - sound
emerges from silence, music of the spheres becomes audible and recognizable on the basis of
homology.
Pythagoras, in fact, established the numerical basis of acoustics. The generalizations of
intervallic proportionality were also applied to dance, sculpture and architecture. The visual
arts follow proportionality defined by the golden section, tetragonal figure designed on the
14
basis of Pythagorean numeric ratios. Pythagorean conception of cosmic harmony influenced
Neo-Platonists, astronomers, astrologers, humanist scholars, poets and musical theorists. His
thoughts, as driven on by his followers, traveled in two directions: those who followed his
mathematical conception and those who followed his ethos theory (Harap, 1938).
15
Plato’s World-Soul
Prior to number becoming a matter, the idea appeared. Platonian idea provides a
sophisticated plan for numeric underpinning of the material world. It is believed that all of
Plato’s (c429 - 347 BC) authentic writings are preserved. The most remarkable sources of his
thoughts on music are Timaneus, Laws and Republic. However, Plato mentions the term
music (mousike) in many places in his dialogues and the meaning of this term may vary from
often condemned sensual pleasure to speculative music as a supreme wisdom (Fubini, 1990).
The immense range of Neo-platonic sources also accounts for the further development of his
ideas during the Middle Ages and Renaissance.
Generally, Plato was continuator of two Greek conceptions of music: (i) the
Pythagorean numeric ontologism and (ii) the Damonian doctrines of musical ethos. Plato’s
approach to music was marked by his tendencies of searching the ideal social structure. Thus,
he implemented the ideas about music into wider context of education and politics. He was a
traditionalist, censorious towards the individualism in ‘modern’ music, which might break
integrity of the society. On the contrary, he viewed the traditional music as acieraging the
society, having a collective character and therefore being an important element of the social
sustainability. Plato criticized decadent style of music, apparently in practice in Greek society,
which he perceived as corruptive, threatening the social welfare of society. These ideas about
the social role of music are explored on the background of musical ontology, which is the
synthesis of Pythagoreism and Plato’s doctrine of ideas, particularly the doctrine of the world
soul as a universal plan of all things described in Timaneus.
In his Laws, Plato provides the first epistemological antimony between rationalism and
sensualism, when criticizing astronomers for theirs methods of verifying the arguments
through sensual experience. However, his rationalism is not well marked but is rather based
on intuitivism and mysticism. The most remarkable of all Platonian thoughts is undoubtedly
the doctrine of the ideas. Ideas are non-material archetypes, primordial prototypes, invariable,
perennial units that are qualitative superior to all phenomena and subjects of visual and
sensible world, which is only the imperfect imitation of them. Whereupon the reality is
divided into two spheres: (i) world of ideas, which are the primordial existence - an
16
ontological basis of all phenomena and (ii) world of spatial-temporal phenomena, which can
be recognized through the senses. The Platonian ontology can be summarized in four basic
premises:
• All things have an autonomous existence.
• The ontologisation of the notion: the subject of every notion has to be the idea - an
inalterable being.
• The hypostasis of the notion: notions exist outside the world.
• The knowledge has rational nature and not sensual in terms of recalling the divine
substance settled in the human soul.
The first preserved formulations of the theory of cosmology can be found in Plato’s
Timaneus (the word ‘music’ is not mentioned, but Plato used the term ‘harmony’, Kinkeldey,
1948), and in his Republic. The Plato’s view on Cosmos was based on the same assumptions,
but differs from that of the Pythagorean view in some details. The main difference is that
Plato defined the model for physical universe - a world-soul, as mediation between numerical
base of all things and physical universe. Therefore numbers became a matter through world-
soul, which is constructed in accordance to a numeric plan. The physical lay-out of the
universe is very similar to that of the Pythagorean one. The whole universe has a shape of
globe as the most perfect form in terms of symmetry. Cosmos consists of eight circular orbits
- spheres: the first sphere consist of fixed stars running in opposite direction to the others, the
second is occupied by Saturn, follows by Jupiter, Mars, Mercury, Venus, Sun, and the eight
sphere is occupied by Moon.
And of each of its circles there was seated a Siren on the upper side, carried
round, and uttering a single sound on one pitch. But the whole of them, being eight,
composed a single harmony. (Republic, X, 614b-619b, translated by Thomas Taylor in
The Works of Plato, London, 1804, vol. I, pp. 466-75., IN: Godwin, 1986).
Therefore the individual spheres are not producing basis for musical ‚cosmic scale‘,
but are moving in harmonious proportions. Godwin (1986, p.3) suggests that:
If we allow that these “spheres” may represent not only the physical orbits of
the planets, but also the powers of those planetary archetypes - the Mercurial, the
Solar, etc. - within the human soul itself, then the journey [journey of souls described
in the Myth of Er] takes on new meaning as an inner pilgrimage through the layers of
17
the psyche to the divine center within, which is also the all-encompassing
circumference of the Spirit.
This may hint at possible contemporary conceptions of astrology, reflecting very close
relations between macrocosm and microcosm and the universal validity of the basic creative
principles displayed through the visible cosmos.
The universe, human beings and also music are built upon the world-soul, in
accordance to its harmonious proportions. The structure of the world-soul consists of the two
basic numerical ratios: 1:2, 1:3 and of their squares, which constitute the basic numerical
consequence: 1, 2, 3, 4, 8, 9, 16, 27, 32 and so on. This sequence can be divided into two lines
according to double or triple squares ordering from 1 to 729 (Dykast, 2005):
2 4 8 16 32 64 128 256 512 1
3 - 9 27 - 81 243 - 729
Table 4.
The number one represents the fundamental number from which all other numbers are
generated. The ascending sequence of these numbers (1, 2, 3, 4, -, 8, 9, 16, 32, -, 64, 81, 128,
243, and 256) constitutes the numeric plan of word-soul expressed in numeric ratios:
1:2:3:4:8:9:16:27:32:64:81:128:243:256
The individual ratios of this sequence determine the musical intervals:
1 = unison 64:81 = major third
1:2 = octave 81:128 = minor sixth
2:3 = fifth 128:243 = major seventh
3:4 = fourth 243:256 = half-tone.
4:8 = octave
8:9 = whole tone
9:16 = minor seventh
16:27 = major sixth
27:32 = minor third
32:64 = octave
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The last two numbers are not included in the world-soul, because their ratio 512:729
defines diminished fifth which is the delimitative point for acceptance. The first four numbers
of this sequence are, in fact, the numbers of Pythagorean tetractys. In general, the closer the
ratio is to its source (number 1) the more perfect is the ratio and the more plausible is the
musical interval based on it.
The fact that ratios of world-soul can be applied to determine the musical intervals
indicates the ontological status of music and its inextricable link to mathematics. In
accordance to Platonian doctrine, audible music is just imperfect imitation of music of the
spheres, music that rests in the ‘silence’ of world-soul. On the contrary, inaudible music is
expression of harmony and symmetry and can be considered as a general quality of
phenomena, and as a desirable state of human soul. Thus, musician is not only the one who
plays or sings, but also the one who has reached the ‘perfect harmony within his soul’ (Fubini,
1990, p.39) and who has acquired the capability of higher understanding closer to vision of
the subject-matter. Moreover, playing the instrument does not necessarily mean performing,
but has the symbolic meaning:
The lyre ultimately became a popular symbol of the harmony of the cosmos. It
appears in the hands of Muses, or Eros, or Orpheus... The lyre becomes the means for
harmonizing the cosmos, and the figure that governs the cosmos rules it by playing the
seven strings of the lyre, harmonizing the seven spheres. (Meyer-Baer, 1970, p.68)
Nevertheless, Plato understood music as being in a close juncture with the other arts:
poetry, dance and theatre. Music is audible and non-audible (as sound and silence)
representation of world-soul’s numeric proportions. Each art displays the same proportionality
in different way. However, Plato proposed ontological contrast between material and non-
material, visible and non-visible, audible and non-audible world through antimony of idea and
matter on the same numerical base. Platonian ontological hierarchy can be designed as
follows:
• Number: ratios, mathematical formulation - analogous to probable patterns of
oscillation of the string, which is the most fundamental known particle in physics.
• Idea: primordial prototypes - analogous to genetic patterns.
• Matter: audible and visible things - analogous to spatial-temporal phenomena.
Plato believed that music has a magic influence on human soul. Every human soul has
been wandering in supernal world of ideas and numeric entities before its birth (this can be
19
understood in terms of modern science as ‘genetic being’). When came into material and non-
eternal world, the soul is recollecting the past through experience and gradually penetrates
through the layers of the soul analogous to the spheres of the universe. This might be the
aspect of inner journey in the Myth of Er (as suggested Godwin above). ‘The harmony within
music echoes the harmony within the soul, and at the same time the harmony of the whole
universe‘ (Fubini, 1990). The motion in music is corresponding to the motion within the
human soul and therefore music has not primarily the function of entertainment but serve as a
tool for refinement of the human affects and for the ethical improvement. Thus music rounded
out the divine plan in humans. Platonian tradition came to Middle Ages as the antinomy of
idea and matter, soul and body, and became transformed by Christian conception of world-
view as being synonymous with the terms of good and evil. Therefore Neo-Platonist
philosophers doubted the sensual perception of music and appreciated music as a
mathematical discipline.
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Boethius’ Musica Mundana
The influence of Boethius’ conception of musica on the following generations of Latin
writers on music is undisputable. He is regarded by modern scholars as perhaps the most
profound writer and translator of Greek tradition into Latin culture, needless to say, besides
the other philosophers of the early Christian Age, as were Iambichus of Chalcis, Augustine,
Martianus Capella and Cassiodorus. At first, one question comes to foreground: to which
extend is Boethius translator and compiler of Greek knowledge, or contributor of new ideas
and theories. According to Karpati (1987, pp.6-7) ‘there was no comprehensive work in Latin
which could contain high-level theoretical matter and from which Greek music - theory could
be thoroughly learnt’ at the time of Boethius. Contemporary Roman writings were merely
focused on grammar and rhetoric, in not comparable range to mathematical field, wherein
music was counted. This might be the reason, why Boethius devoted himself to the
mathematical disciplines. He put the four mathematical sciences under the umbrella term
quadrivium (‘quadruvio vestigatur‘, chapter: Proemium, in quo divisio mathematicae, De
institutione arithmetica, book I) for the first time, and which includes arithmetic, geometry,
astrology and music. He regarded arithmetic as the superior discipline to the others:
Quae igitur ex hisce prima discenda est nisi ea, quae principium matrisque
quodammodo ad ceteras obtinet portionem? Haec est autem arithmetica ... ut animal
prius est homine (De institutione arithmetica, book I).
One might expect that the first of his writings was De institutione arithmetica, which
is written after Nichomachus’ work on arithmetic reflecting Pythagorean view of ontology. It
is not known whether he wrote also about geometry and astrology, but treatise on music De
institutione musica is preserved, even incomplete (five books preserved from supposed
original seven books), and become the most quoted treatise on music during the Middle Ages.
De institutione musica is probably written after Nicomachus’s lost work on music
Introduction to music and the fifth book is a compilation of Ptolemy’s Harmonics. His treatise
is a synthetic work reflecting Neo-Pythagorean and Neo-Platonic tradition. He understood
music as a pure theoretical discipline - philosophical speculation. Counting music as a
quadrivium discipline he contributed to music theory in terms of mediaeval systematical
21
knowledge and his Latin typology of music based on Greek cosmology become the general
theoretical framework of mediaeval concept of music theory. This background information is
important for proper understanding of different methodology of music.
The concurrence of various disciplines, particularly those of quadrivium, in one
common universal knowledge, simply imply that his thoughts about music should be scanned
not only in De institutione musica, as it is usually realized, but as Chamberlain (1970)
correctly suggests, also in other sources, notably in De institutione arithmetica and in
Consolatio philosophiae. According to exploring the ontology of music, we can found
fragmentary information in De institutione musica as Boethius himself noted that he will
provide the further explanations of musica mundana and musica humana, but he did not
mention where. Boethius, analogous to Pythagoras and Plato, understand numbers as
primordial principle. According to his Christianity, of course, numbers become the primary
tool of creation:
...Conditor deus primam suae habuit ratiocinationis exemplar et ad hanc
cuncta constituit, quaecunque fabricante ratione per numeros adsignati ordinis
invenere concordiam (De institutione arithmetica).
The fact that numbers are construed as primordial beings is also important for
ontology of music as the musical intervals are derived from numeric ratios. In chapter De
substantia numeri he states that ‚omnia quaecunque a primaeva rerum natura constructa sunt,
numerorum videntur ratione formata.‘ Therefore Boethian conception of music is based on
mathematical underpinning of nature and influenced by methodology of quadrivium, which
reflects the analogy of epistemological organon to the four senses, four seasons, four
elements, and to the four creatures below the throne of God. It means that there are four ways
how to approach to the reality according to hierarchy of quadrivium:
• Arithmetic: ontology - superior to all phenomena
• Geometry: pure forms - spatial phenomena
• Astrology: cosmos - spatial-temporal phenomena
• Music: perceivable quality of spatial-temporal phenomena
Boethius, probably under the influence of Aristotle, emphasizes the sensual dimension
of music and considers the ability of perception through the senses as a natural attribute of all
22
‘living creatures’. However, he assumes that perception itself is linked to the mind rather than
to the object and poses ontological issue:
It is obvious that we use our senses in perceiving sensible objects. But what is
the exact nature of these senses in connection with which we carry out our actions?
And what is the actual property of these objects sensed? The answers to these
questions are not so obvious; and they cannot become clear to anyone unless the
contemplation of these things is guided by a comprehensive investigation of reality.
(De institutione musica, Introduction, IN: Godwin, 1986, p.44)
As Woodcock mentions (1943, p.32), ‘The battle between reason and the senses still
rages.’ Boethius presumes that through the mathematics it is possible to gain the
understanding of the essence of all sensually perceived phenomena:
...if someone sees a triangle or square, he can easily identify it by sight. But
what is the essence of a triangle or a square? This he must learn from a mathematician
(Godwin, 1986, p.44).
But when hearing, perceived sounds are not only recognized in terms of their
structure, but also in terms of aesthetic judgment made by subject. This may be plausible ‘if
the are in the form of sweet and well-ordered modes’, or implausible ‘if the sounds heard are
unordered and incoherent’. Therefore, as Boethius states, the other disciplines (quadrivium)
are related to ‘the investigation of truth’ and music to speculation and morality: ‘musica vero
non modo speculationi verum etiam moralitati coniuncta sit‘. The basis for such an aesthetic
judgment is considered in fact that ‚amica est enim similitudo, dissimilitudo odiosa atque
contraria‘. This can be understood as ‚the principle of similarity‘ between the structures
within the subject and perceived object who are supposed to have, consequently, generic
numerical origin. With accordance to ‚the principle of similarity‘, as it was explaned by Neo-
Platonists Plotinus, Boethius clearly adopt Plato’s ethos theory:
For there is no greater path whereby instruction comes to the mind than
through the ear. Therefore when rhythms and modes enter the mind by this path, there
can be no doubt that they affect and remold the mind into their own character.
(Godwin, 1986, p.45)
The ethos theory is unavoidable consequence of hierarchy of phenomena and of
generic numerical underpinning of the reality. Music is presupposed being everywhere, in
both macrocosmic and microcosmic dimensions. Thus Pythagorean and Platonic thoughts
about music and cosmology are prerequisites for Boethian classification of music. This,
23
perhaps the most quoted classification of music in mediaeval literature, can be found not only
in De institutione musica, but as Chamberlain (1970) suggests, the other relevant definitions
can be found in Consolatio. Either few further explanations can by drawn from De institutione
arithmetica. Boethius describes in De institutione musica three types of music (Tres esse
musicas): musica mundana, musica humana and musica instrumentalis. This typology is not
quantitative, but either qualitative in the terms of dimensional ontology. Thus the music
mundana and humana have different ontological status as instrumentalis. Musica
instrumentalis is in its definition closest to the modern term of music and therefore is not
further explained in this essay. On the contrary, the two other types of music are disputable in
terms of ontology. Musica mundana includes three distinctive forms:
‘The first type [musica mundana], that is the music of the universe, is best
observed in those things which one perceives in heaven itself, or in the structure of the
elements, or in the diversity of the seasons’. (Godwin, 1986, p.46)
Either according to Consolatio (Chamberlain, 1970), musica mundana consists of
three forms or categories:
1. Motions of celestial bodies - not audible for human ear.
2. The binding of the elements - inaudible harmony.
3. The alteration of the seasons - inaudible.
In De institutione arithmetica Boethius explanes the generic numerical base for
elements, seasons and celestial movements: ‚Hinc enim [numerorum ratione formata] quattuor
elementorum multitudo mutuata est, hinc temporum vices, hinc motus astrorum caelique
conversio‘. However, Boethius does not distinguish the category of sound in such ontological
hierarchy as the types of the musicas themselves. This regards the first type of musica
mundana:
How could it possibly be that such a swift heavenly machine should move
silently in its course? And although we ourselves hear no sound - and indeed there are
many causes for this phenomenon - it is nevertheless impossible that such a fast
motion should produce absolutely no sound, especially since the orbits of the stars are
joined by such a harmony that nothing so perfectly structured, so perfectly united, can
be imagined. (Godwin, 1986, p.46)
Chamberlain (1970, p.82) assumes that ‘the philosophic tone of this music, like that of
the world, would seem to be largely physical and mathematical’. This confirms that Boethius
24
emphasizes the perceptual aspect of hearing and construed it as a part of ‘world music’. Thus,
as Woodcock (1943) suggests, evaluation of consonance depends on both ear and science.
In De institutione musica he only poses questions with regard to musica instrumentalis
but does not provide a satisfactory answer:
For what unities the incorporeal existence of the reason with the body except a
certain harmony (coaptatio) and, as it were, a careful tuning of low and high pitches in
such a way that they produce one consonance? What unites the parts of man’s soul,
which, according to Aristotle, is composed of a rational and irrational part? In what
way are the elements of man’s body related to each other or what holds together the
various parts of his body in an established order? (Godwin, 1986, p.47)
However, with reference to Consolatio, musica humana, similarly as mundana, has
three forms, too (Chamberlain, 1970, p.82):
1. ‘The fit proportioning or blending (“coaptatio” and “temperatio”) of the
“incorporeal life of reason” with the body, like one musical consonance of high
and low notes’.
2. The second ‘is the joining of parts within the soul itself, of rational and irrational
parts’.
3. The third ‘is both the thorough mixing of the elements and the fixed proportioning
of members in the body alone’.
This type of music is inaudible, and therefore rests in silence. Boethian conception of
musica humana is far from simplification that of the harmony between the body and soul. It
indicates the structural convexity within the living system on the basis of highly sophisticated
mediation which Boethius assumes being conveyed by mathematical proportions. The four
basic elements of genetic information and their combinations are the basic constituents of
such living system - a microcosm itself, what seems being analogous to Pythagorean tetractys
as the source of macrocosm. Boethius was much more Pythagorean as it is thought according
to his treatise De institutione arithmetica. His classification of music should not be
understood literary, but through the background information of arithmetic, numerology, Neo-
Pythagorean and Neo-Platonic mysticism.
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Kepler’s Planetary Polyphony
Johannes Kepler (1571-1630), German astronomer and philosopher, was the last
adherent of Greek tradition of Music of the spheres. His prolific and courageous attempt was
to link together the idea of harmonious organization of the cosmos and the latest astronomical
observations based on empirical data. However, Kepler’s first great work Mysterium
Cosmographicum (1596) reflects deviation from Ptolemaic cosmological theory in favor of
the heliocentric theory of planetary motion invented by Nicolaus Copernicus. The
contemporary astronomers, such as Galileo Galilei, and Tycho de Brahe, took advantage of
modern telescope equipments due to the improvement of optics. In 1600, Kepler became the
assistant to Brahe in well-found astronomical observatory in Prague. After the death of Brahe
in 1601, he assumed his position as court astronomer and mathematician to Rudolf II, and he
had opportunity to use the most modern telescope in that period.
Kepler sketched a comprehensive hypothesis of geometrical organization of planetary
motions and distances among their orbits. He knew only five planets: Saturn, Jupiter, Mars,
Venus, and Mercury. If there are included also Sun, Earth, and Moon, it is similar planetary,
respective spherical, system as in Greek cosmology. However, the role of deities has shifted
under the influence of new theories and observations. The spherical motion focused around
the Earth became the orbital motion of particular planet around the Sun and was not
autonomous henceforward. The Sun became not only the center of this new view of cosmos,
but he considered it as the basic motive power which decreases proportionally with the
distance of particular planet from the Sun. Later on, Isaac Newton established his theory of
gravitational force on Kepler's theories and observations.
During his service on the court of Emperor Rudolf II he wrote one of his major works
Astronomia Nova (1609). This work contains formulations of two of so-called Kepler’s three
laws of planetary motion, which are best known nowadays, although Kepler himself regards
his explanations of ‘world’s harmony’ more important than his formulations of the three laws
of planetary motions (Brackenridge & Rossi, 1979). The first law is that he discovered the
planetary orbits have to be elliptic and not circular as he had presupposed before. The Sun is
stationary focus of these elliptic orbits. The second law states that an imaginary line from the
26
Sun to a planet terminates equal areas of an ellipse during equal intervals of time, accordingly
an orbital speed of a planet is not constant and depends on distance from the Sun: the closer a
planet comes to the Sun, the more rapidly it moves. The formulation of the third law was
introduced in Harmonices Mundi (1619), it states that the ratio of a cube with face equal to a
planet’s distance from the Sun and the square of the planet’s orbital period is a constant valid
for all planets.
According to his discoveries, Kepler believed that the universal harmony could be
found in planetary structure. He devoted himself fully to research the geometrical laws
accountable for distribution, organization, and motions of celestial bodies. In The
Cosmographic Mystery he posed the question why there are only five planets in the solar
system. He found the reason in the fact that there are only five regular three-dimensional
solids with identical faces all joined with identical angle. These solids are: (1) Cubus, (2)
Tetrahedron, (3) Dodecaherdon, (4) Icosihedron, and (5) Octohedron. In the fifth book of
Harmonices Mundi, De harmonia perfectissima motuum coelestium, chapter De quinque
solidis regularibus he drew a parallel between the intervals among the planetary spheres and
these regular solids in following order: Saturn - cube - Jupiter; Jupiter - tetrahedron - Mars;
Mars - dodecahedron - the Earth; the Earth - icosihedron - Venus; and Venus - octahedron -
Mercury. Further investigation proved that data fits only approximately and not exactly.
Nevertheless, Kepler believed that ‘God the Creator is the Geometer and speaks in the
universal language of geometry’ (Brackenridge & Rossi, 1979, p.113).
The Keplerian geometrical forms, which are in basic correspondence to musical ratios,
are derived from astrology. It comes to this that the layout of two particular planets or stars
forms a geometrical or a non-geometrical angle by connecting the imaginary vectors of these
bodies with the Earth. (Brackenridge & Rossi, 1979) A harmonic angle is the angle derived
from one of eight harmonic ratios of motion (0o, 60o, 72o, 90o, 120o, 135o, 144o, and 180o;
schemes):
27
Table 5. (according to Brackenridge & Rossi, 1979, p.114)
Implicitly, these harmonic angles are indubitable due to inevitability of their causal
existence, but their interpretations are axiomatic. The circle is divided by inscription of
regular polygons into identical fragments, which constitute the ratios and angles, as it is
presented in the schemes above. These angles and ratios implied from them are the basic
terms of astrological interpretation of planetary constellation:
Constellation conjunction opposition trine quartile sextile quintile biquintile sesquaquadrate
Angle 0o 180o 120o 90o 60o 72o 144o 135o
Interval unison octave fifth fourth minor
third
major
third
major
sixth minor sixth
Ratio 1:1 2:1 3:2 4:3 6:5 5:4 5:3 8:5
Table 6.
Kepler wrote: ‘Perhaps God himself has invariably expressed these proportions
[regular polygons inscribed into circle] in bodies and motions’ (Harmonices Mundi Lber III,
28
Source: Godwin, 1986, p.149). He accepted all the harmonic ratios derived from harmonic
angles as musical consonances, in accordance to music theory of early 17th century.
Kepler at first had believed that planets’ orbits are circular, but latter the observations
data did not fit to this assumption and hint on the new theory that these orbits have to be
elliptic (the first law of planetary motion) and therefore ‘imperfect’. This imperfection must
have some reason and Kepler proposed a bit curious hypothesis: each planet does not
represent particular tone (because the distance from the Sun is not constant) but melodic
pattern in dependence of the range between the aphelius (farthest point from the Sun) and
perihelius (closest point from the Sun) distances. This hypothesis of music of the spheres was
new at all and based on empirical data. He adjudicated the musical scale – the fundamental
sequence of ascending and descending notes for each planet in correspondence with their
elliptical orbits, and within the range equal to the deviation of perihelion and aphelion
distances:
Table 7.
The individual notes of these melodic patterns are selected points of permanently
changing pitches (in terms of ‘planetary glissando’) within its range. The closer is the planet
to the sun the higher is the pitch. The lowest note of each pattern represents aphelius point,
the highest note perihelium. Therefore each pattern repeats simultaneously with one orbital
period which is different for each planet (according to Kepler observations presented in
Harmonices Mundi): Mercurius 87 days, Venus 224, the Earth 365, Mars 686, Jupiter 4332,
and Saturnus 38769 days. The ‘musical’ range is very small in the case of Earth’s orbital
course - only the semitone – mi fa. According to Kepler’s interpretation, the semitone sounds
29
sad, and symbolizes the decline and corruption of earthly sphere with its imperfection (misery,
famine, Gamwell, 2002). Forasmuch as each planet has its own melodic subject, the music of
the spheres, of Musica mundana, has to be polyphonic. Walker (1967, p.232) noted that:
For Kepler just intonation and polyphony had finally prevailed because they
were natural, that is, they corresponded to the archetypes in the mind of God, on
which the created world was modeled, and which are also in the mind of man, the
image of God.
Kepler’s intention was primarily not focused to prove celestial music, but to find and
prove harmonic proportions of planetary system in terms of their spatial and temporal
organization. His speculations about music were based on astronomical research and
astrologic interpretation of the universe. Is the Keplerian analogy among the regular solids,
harmonious angles and musical consonances a metaphor or a real correspondence between the
macrocosms and unifying principle based on universal harmony? Majority of Kepler’s
observations and conclusions are valid till nowadays, but his ‘cosmic polyphony’ is symbolic,
because he did not believe that celestial harmonies are audible: ‘The source of the human
response to music is to be sought in the soul and intellect, not in physical matter’ (Harmonices
Mundi Lber III, Source: Godwin, 1986, p.149). The important part of Kepler’s theories about
music is his interpretation of a sound:
How a plucked string will transfer its sound to another unplucked one if they
are consonant with one another, but leave it immobile if they are dissonant. Since this
cannot be the work of any mind, because a sound thus caused has neither mind nor
intellect, it follows that we must say that it is caused by a simultaneity of motions... If
the speed of one string can serve to move the other one tuned to it, though it be
untouched as far as the eye can see, will not the same speeds of both strings serve for
the pleasant stimulation of the ear, because the latter is in some way moved uniformly
by the two strings, and two impulses from the two sounds or vibrations meet at the
same moment? (Harmonices Mundi Lber III, Source: Godwin, 1986, pp.150, 151)
The medium of transferring particular vibration Kepler took as species immateriata -
the etheric emanation from object. Movement of e.g. a string causes this phenomenon. If a
string of particular length and tension is potentially influenced by species immateriata, then it
would be perhaps possible to transfer the powerful cosmic vibrations into human mind. The
idea of simultaneity of motions was later treated by Athanasius Kircher in his great work
Musurgia Universalis (1650). He described an imaginary instrument ‘enneachord of nature’
on which every string, if plucked, resounds through all levels of the beings.
30
PART TWO: POST-COSMOLOGICAL CONCEPTIONS
As soon as philosophy became an autonomous discipline, by the result of establishing
the positive natural sciences based on empirics during the 18th and 19th centuries, the
metaphysic dimension of music was apprehended in separation from theory and practice of
music, and from other sciences such as astronomy, mathematics and physics. Jean-Philippe
Rameau noted in Preface to his remarkable Treatise on Harmony (1722):
However much progress music may have made until our time, it appears that
the more sensitive the ear has become to the marvelous effects of this art, the less
inquisitive the mind has been about its true principles. One might sad that reason has
lost its rights, while experience has acquired a certain authority. The surviving
writings of the Ancients show us clearly that reason alone enabled them to discover
most of the properties of music. Although experience still obliges us to accept the
greater part of their rules, we neglect today all the advantages to be derived from the
use of reason in favor of purely practical experience... Conclusions drawn from
experience are often false, or at least leave us with doubts that only reason can dispel
(Rameau, 1722/engl. ed. 1971, p.xxxiii).
Contrary to the cosmology of music, where all disciplines were integrated in their
methodology, the disciplines of modern science forked into arts and exact science. The
methodology used in post-cosmological conceptions of musical ontology stems from
philosophy: (i) epistemology, concerned with role of subject in cognition, (ii) ontology
focused on subjective perception in terms of a priori givenness, and on the objectivity of
music. Therefore the ontological issues lost their simplicity based on common premises, and
became sophisticated disputes trying to comprehend the complexity of all phenomena and
provide an acceptable paradigm for them.
Metaphysic of music is apprehended from various points of view, represented by three
subjects selected: (i) Immanuel Kant’s integration of rationalism and empirics, his rejection of
metaphysics, (ii) Arthur Schopenhauer’s ‘modern’ cosmology understanding music as a
‘direct copy’ of everything-penetrating will, and (iii) phenomenology of music providing
31
several solutions of the ontological issue. Music was apprehended as a perceptual
phenomenon, i.e. subjective perception of objective sound concepts. The metaphysic
dimension of this perception was sought no more in cosmology but in human subject.
However, the antimony of silence and sound became less and less recognizable and a new
antinomy appeared: objective sound and perceived sound. The inaudible music of universe
was lost.
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Immanuel Kant: Mind as a ‘string instrument’
One of the most influential philosophical theories concerning metaphysics and
transcendental aesthetics was set up by Immanuel Kant, notably in his writings The Critique
of Pure Reason (1787) and The Critique of Judgment (1790). Although Kant is not generally
regarded as ‘philosopher of music’, his contributions in the field of epistemology (rational and
empirical), relations of cognition and perception, explanations the categories of object and
subject are indisputable. The consequences of his proposed ideas on philosophy and aesthetics
of music became essential concepts for following generations of scientists and philosophers.
His works, especially the three of Critiques, are a bridge between rationalist and empiricist
traditions.
Kant stated what was formerly indicated by Descartes, that objective knowledge can
be apprehended exclusively as a consequence of the cognitive acts of a subject. Rational
human subject is situated in the centre of cognition. Although he understood the aesthetics as
a science concerning the perceptional quality of objects, rational order of the world could
never derive from accumulation and organization of sensual perceptions. While in traditional
cosmological theories the human subject is a part of whole universe, a mirror of it,
‘microcosmical representation of macrocosm’, and therefore the same rules are applied for
them, Kant drew a methodological difference between them, and not a parallelism.
Consequently, ‘...he situates beauty not in the object but in a psychological experience of the
subject: the “determining ground” of the beautiful “can be no other than subjective” (Reed,
1980, p.566).
If the intelligibility of objects in the world can be brought about only via
synthesizing acts of the mind, the mind can no longer be just the imitator of pre-
existing objects... Kant rejects claims about nature's inherent structure, arguing that we
ourselves ‘give the law’ to nature as it appears to us, so that we cannot know nature as
it is ‘in itself (Bowie, 2006).
This is the most fundamental contradiction to cosmology of music. The correlation
between the human being and the universe has categorically been changed. Kant made a
separation of ‘supersensible realm’ from phenomenal world. Therefore, his conception of
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transcendental aesthetics (Critique of pure reason) does not presuppose any ‘existing forms of
beauty, whether natural or artificial’ (Reed, 1980, p.568). The gateway to understanding lies
in exploration of cognitional facility of a man. Thus ontology of music is concerning with the
human subjectivity, especially in its pure form of cognition.
He made a distinction of the knowledge into (i) categorial (a priori): pure without
addition of empirics, independent from experience and impressions; (ii) empirical: originated
in experience. He noted out that even if any knowledge does not anticipate experience in
terms of temporality, knowledge itself is not entirely originated in experience. This
contradiction is resolved by the fact that the quality of our cognitive faculty contributes by
itself to knowledge. The mathematics serves as an example that a priori recognition is
possible without the dependence of experience, even though mathematical judgments
themselves are synthetic. Therefore reason is faculty providing a priori principles of
knowledge.
The transcendental knowledge, about to be a priori possible, is concerned with no
objects or phenomena, but with the process of our recognition of objects. The objects are
given to us through the medium of the senses which provide us with perception. A pure form
of this perception is possible to deduce as follows: if we eliminate from the representation of a
solid (i) what reason thinks about it, and (ii) sensations like color, impenetrableness etc.; the
remanentia of the representation are shape and spatial dimension (Kant: Critique of pure
reason). Similarly, the time is not regarded as empirical notion derived from experience,
because we could not perceive the actual time and the consecutive time if they are not based
on a priori notion of time. Therefore space and time are essential notions, substances of all
perceived sensory data. These substances are not autonomous as well as attributes of
phenomena, but are the form, an ‘inner sense’ of a man’s perception. As a result of
implication this theory into ontology, the ‘real world’ was split into (i) phenomena -
appearances, experience, and (ii) nomena - things themselves. All of the nomena are
incognosible, thereupon the existence of primordial musical structures are rather uncertified.
On this account, the existence of music, or musical phenomena, is conditional to human mind.
However, Kant was rather skeptic about music as a mind becoming phenomenon. In
his Critique of Judgment, §51 ‘Of the division of the beautiful arts’ he proposed the
classification of the fine arts into three categories: ‘the arts of speech’ - rhetoric and poetry;
‘the formative arts’ - sculpture, architecture, and painting; and ‘the art of the play of
sensations’ - Tonkunst. The first two categories present no analytical problems, but in the
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third (play of sensation: tone and color) Kant finds that there is no certain utterance whether
colors and sounds consist of disordered bundles of sensations, or possess determinate forms:
If we think of the velocity of the vibrations of light [color] or in the second
case of the air [tone], which probably far surpasses all our faculty of judging
immediately in perception the time interval between them, we must believe that it is
only the effect of these vibrations upon the elastic parts of our body that is felt, but that
the time interval between them is not remarked or brought into judgment; and thus that
only pleasantness, and not beauty of composition, is bound up with colors and tones.
(Kant, §51, p.169)
This statement is like to be a ‘phenomenological’ analysis of composition, the same
issue employed medieval writers on music, but in rather different conception in ‘grammar of
music’ (add reference!) The issue was related, similarly to Kant, to the question whether
music consists of some kind of dividable commposita or not, et inde whether music is art
conveying particular meaning or not. Parret (1998, p.260) on this account suggests:
It is clear that music requires no activity of thought, since it has no semantic
component: a musical sequence has no propositional content such as is found in
language (including the most “beautiful” language possible, namely poetry). Music
does not make us think; rather, it causes us to reflect and to dream more than any other
art.
According to this task, Reed (1980, pp.569-570) mentioned the problem of the nature
of sound in connection with the first and second editions of the Critique: ‘In the first he
[Kant] says “ich zweifle gar nicht” that sound vibrations possess a form, but in the second he
says “ich zweifle gar sehr”. If sound vibrations have a form, than it would be possible make a
judgment and music would be considered as fine art. Kant offered a compromise: music
possess to a particular extend both form and sensation. However, Kant placed music at the
lowest place among the other arts ‘because it merely plays with sensations’ and therefore is
not constituted in pure rational acts (see phenomenology of music):
The formative arts produce ‘lasting impressions (Eindrücke),’ while music
produces only ‘transitory impressions’. And this oscillating degree of presence
appears to be related to the difficulties Kant has had in situating music in his analytical
categories. However, both comments are governed by a structure that continually
discounts the worth of music with respect to that of the bildenden Künste, which thus
represent a kind of mean of presence (even though we are to take no ‘interest’ in their
existence) between a glut and a dearth. (Reed, 1980, p.575)
35
It seems to be paradoxical that Kant understood music as sound and perception, and
the fact that music have from this point of view transitory, not lasting existence, led him to
exclude music from rational speculation and therefore he abases music as an formative art.
His theory lacks some kind of ‘higher paradigm’ of music (e.g. cosmology) in terms of
rational rule that would be able to confer judgments about its quality. However, music is still
a cultural phenomenon in that it proposes to human beings new orders of perception.
While music is abased as a play of sensation not conveying rational form, the
cognitional faculty of a man itself can be understood in ‘musical’ terms. Kant often used in
his Critique of Judgment such terms as ‘harmony’, especially ‘harmony of cognitional
faculties’ in accordance to the ability of aesthetic judgment. Both Reed (1980) and Parret
(1998) proposed a speculative (at least) interpretations of Kant’s text:
When one takes account of the materiality of Kant’s text, it is evident that for
one of the most complicated elements of his terminology, Gemüth, musical imagery is
omnipresent: the mind (Gemüth) is presented to us as itself a musical instrument, more
specifically a stringed instrument. The same thing could be said of the Anthropologie,
where sensibility, as the first property of the mind, is presented as a bodily organ on
which something like music is played. (Parret, 1998, p.262)
Kant thus imagines the mind as a sort of musical instrument, more precisely a
stringed instrument (or perhaps the psychological equivalent of the vocal chords), the
principle strings being understanding (shown vibrating here), reason, and imagination.
That is why in the same paragraph he calls a ‘state of mind’ a ‘Gemütsstimmung,’
literally a ‘pitch’ or ‘tone of mind,’ and speaks elsewhere of the ‘beide Gemützustände
zusammenstimmen (two mental tones harmonizing, in accord)’ ([§]16), or a
representation that ‘places the cognitive faculties in a proportionierte Stimmung’ with
each other through its harmony (Zusammenstimmung) with the ‘conditions of
universality’ supplied by the understanding ([§]9). The activity of our cognitive
faculties generally is thus called a ‘Spiel,’ a play of mental strings. Within this
structure Kant defines beauty (that is, the subjective experience of something as
beautiful) as the mental tone that results from the harmonious interplay of the string of
imagination and the string of understanding. (Reed, 1980, pp.579-580)
It is improbably that Kant’s intention was to hint on this interpretation deliberately.
However, are then the proportion and the functionality of human mind, determined by
‘general rules of harmony’, an a priori attribute of pure reason? Is the harmony an a priori
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unconscious presumption of mind in like manner as time and space are conscious? The
question Kant asked himself is:
...in what way we are conscious of a mutual subjective harmony of the
cognitive powers with one another in the judgment of taste - is it aesthetically by mere
internal sense and sensation, or is it intellectually by the consciousness of our designed
activity, by which we bring them into play? (Critique of Judgment, §9)
If ‘the given representation’ activating through our senses the judgment of taste, was
concept ‘uniting understanding and imagination’, the ‘consciousness of this relation would be
intellectual.’ But, as Kant later mentioned, this kind of judgment is not that one of the taste,
because it lacks reference to ‘pleasure and pain’. On the contrary, if the ‘subjective universal
communicability of the mode of representation in a judgment of taste’ is possible to
presuppose without particular concept, then it should refer to ‘nothing else than the state of
mind in the free play of the imagination and the understanding.’ Therefore the basis for
aesthetic judgment is not a ‘concept’ but ‘harmony’:
This merely subjective (aesthetical) judging of the object, or of the
representation by which it is given, precedes the pleasure in the same and is the
ground of this pleasure in the harmony the cognitive faculties. (Kant, Critique of
Judgment, §9)
In the original text, Kant used in many places in stead of the term ‘harmony’ -
Harmonie, other, quite synonymic terms such as Zusammenstimmung, Einstimmung,
Übereinstimmung, or Beistimmung. (see also Reed 1980, pp.578-579) Although these terms
have apparently no reference to music, the meaning is almost the same as in music,
representing particular dynamic correlation according to particular rules.
Forasmuch as it is not possible to prove the intelligibility of musical perception, Kant
suggested different point on this issue in §54 of his Critique of Judgment. He described the
psychological mechanism of laughter with relation to musical experience. He stated that both
laughter and musical experience are based on corporeal activity with cathartic effect and
therefore cause physical pleasure generated by releasing of a state of tension: ‘Laughter is an
affection arising from the sudden transformation of a strained expectation into nothing.’
(Kant’s italics, 54§) Accordingly, Parret (1998, p.263) suggests that ‘musical experience can
also be described in terms of tenseness (expectation, tension, release).’
One might ask why music represents such methodological problem in Kant’s text. For
this purpose may be useful to design a paradigm with reference to Critique of pure reason.
37
OBJECT
noumenon ‘thing of itself’
BODY
senses, physical equilibrium (principle of laughter)
MIND
cognitive process, phenomena (thinking about objects)
PURE REASON
a priori knowledge, time & space
Table 8.
The pure reason is situated in the center representing the ability of pure knowledge,
and of a priori judgments. The problem occurs if this paradigm is adapted to Critique of
judgment, namely to the aesthetic judgment, and more specific to the judgments about music -
play of sensations. While in the formative arts space (concept, form) and time (lasting
impressions) in the terms of a priori attributes of the pure reason are definable, in music
space (no concept) and time (transitory impressions) are indefinable. Therefore Kant
suggested that there has to be harmony between mind and body - a play of sensations, and
harmony between mind and reason - a harmony of cognitive faculties. However, there is no
subset of pure reason in terms of a priori harmony in Kant’s text, and therefore the harmony
is among the other sets (pure reason, mind, and body) and by this correlation is outside the set
of pure reason.
Generally, Kant thoughts were autonomous, without dictates of external authority. He
designated the methodological difference between the universe of all things and their
temporal and spatial representations in the human subject. Consequently, he isolated the
cognitional options of universe in term of ontology from those in human subject. The music
of the spheres was not a mirrored model for harmony of ‘cognitional faculties’ that were, in
fact, a modification of musica humana. On the contrary, the human subject is a model for
universal harmony:
38
...all of nature must be read in terms of the subject’s mental structure. Or put it
differently, the vibrations of the cognitive faculties spread out and resonate through all
of nature - it being of the nature of music always to extend and impose its existence.
(Reed, 1980, pp.580-581)
Harmony and music became the attributes of interaction between mind and sensual
faculty. The metaphysic aspect of this act is hidden in a priori givenness of the mind.
Therefore, there is no reason to assume that music exists outside this mind, because the
common genesis between the universe and subject is missing. However, Kant’s text, indeed,
presupposes a general assumption of harmony. Whether this assumption is an attribute of pure
(conscious) reason or unconscious general condition of subject, is not possible to define. The
reason for this consists in impossibility of excluding the subjective from unconscious general
condition.
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Schopenhauer: Music as representation of the Will
Arthur Schopenhauer (1788-1860), was one of the first Western philosophers of
modern history who had access to the translations of Indian philosophical treatises, namely
those belonging to Buddhist and Vedic traditions. This fact might have contributed to
formulation of his conception of the ‚will‘, and phenomenal world as its representation. Some
of his thoughts have been undoubtedly drawn from Hindu theory of Maya, notably those of
the illusionary nature of phenomenal world and that people do not have individual wills but
were rather simply part of a vast and single will that pervades the universe, that the feeling of
separateness that each of has is but an illusion. The main core of his philosophical output is
included in his famous work The World as Will and Representation published in 1819 and
later on, the new edition of two volumes published in 1844.
Schopenhauer was to a certain extent follower of Kantian idealism in the terms of
distinction the reality into phenomena and noumena, namely the things as they appear to us
and the things-in-themselves as they are beyond the grasp of a man’s reason. Schopenhauer
negotiated this ontological agnosticism and turned the whole Kantian ontology at new,
metaphysical direction through his interpretation of Kant’s thing-in-itself as ‘will’.
Schopenhauer’s classification of all beings and his view on universe differs from that of the
Kantian in many respects. The thing-in-itself as the will has an active role in its
representations; all phenomena are in dependence of the will’s objectification. The hierarchy
of beings can be simplified as follows:
The universe
appearances = representations of the will
objects
thing-in-itself = will
subjects
ideas (Plato’s ideas) phenomena (space & time)
Table 9.
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According to this table, out of all the categories only phenomena are governed through
a priori attributes (space & time) of pure reason. Experience includes phenomenal world,
appearances and representations. Although experience has a serious ontological problem: how
to recognize the inner nature of things? Schopenhauer mention in his The World as Will and
Representation (trans. E. F. J. Payne, 1969, pp. 98-99):
We want to know the significance of those representations; we ask whether
this world is nothing more than representation. In that case, it would inevitably pass us
by like an empty dream, or a ghostly vision not worth our consideration. Or we ask
whether it is something else, something in addition, and if so what that something in
addition, and if so what that something is.
By the term ‘something else’ Schopenhauer meant ‘inner world’ or ‘inner nature’ of
all the phenomena, id est things out of empirical nature. He apprehended human body as a
physical phenomenon, or ‘physical object among physical objects’ (Alperson, 1981, p.156).
However, self-consciousness represents more than physical phenomena, because it expresses
will: ‘The action of the body is nothing but the act of the will objectified, i.e., translated into
perception’ Human will is ‘knowledge a priori of the body, and that the body is knowledge a
posteriori of the will’ (Schopenhauer, pp. 100-101). This categorization Alperson (1981,
p.156) characterizes as ‘epistemological dualism’.
Schopenhauer apprehended the human being as embodied will and emphased the fact
that the human behavior is subjected to it. The will itself governs a metaphysical dimension of
the world, and therefore confer an ontological status to all its appearances and representations.
The will is a universal principle at the same time in unity with phenomenal world and apart
from it. It is also an essence-mover of the phenomenal world:
One can see the will manifesting itself in the blind forces of the inanimate
world such as gravitation, magnetism, and electrical attraction and repulsion, as well
as in the forces of germination and vegetation in the plant world, and in the
personalities and actions of men. The world is at once will and representation.
(Alperson, 1981, p.156)
The acts of the will’s objectification are in peculiar hierarchy according to complexity
and clarity how they are expressing the will. They are, in fact, Platonic ideas, the ‘original and
unchanging forms and properties of all natural bodies, whether organic or inorganic, as well
as the universal forces that reveal themselves according to natural laws.’ (Schopenhauer,
World, Vol. I, p.169.) Ideas are the archetypes, the individual objects, then, are copied in
41
accordance to them. The hierarchy of the arts is organized in the same order as the hierarchy
of clarity and complexity of the objectification of will. Hierarchy of the arts (from low to
high), according to Schopenhauer:
• Architecture (gravitation, stone material, proportion).
• Painting (landscape painting = imitation of the world of plants; human bodies =
imitation of humans, expression of the man’s character).
• The literary arts (expression of emotions and actions).
• Music has an outstanding position, because ‘in it we do not recognize the copy, the
repetition, of any Idea of the inner nature of the world’. Ideas are the objectivity of
will (see table above); music is not repeating them but will itself and therefore
differs from the other arts repeating the Ideas. Schopenhauer apprehended Plato’s
Ideas apart from world of experience and therefore they are out of knowledge, too.
However, they may become an ‘object of knowledge in aesthetic contemplation’,
particularly in the other arts.
Schopenhauer stated that ‘parts of all harmony’ are the four voices: bas, tenor, alto,
soprano or: fundamental note, third, fifth, and octave, and are in correspondence to ‘four
grades in the series of existences: mineral, plant, animal, and human. Bass ‘moves heavily,
rises and falls only by large intervals, thirds, fourths, and fifths, and is guided here by fixed
rules in each of its steps’, and therefore represents naturally the ‘inorganic kingdom of
nature’, while soprano with ‘great flexibility’ bears the melody and represents the ‘highest
stage of the scale of beings’. So, the hierarchy of parts in music reflects the hierarchy of the
other arts. Music itself is an independent art, has its own resources.
Another issue Schopenhauer was concerned with is the combination of music and text
in vocal music and opera. The relationship of tone and speech or music and poetry is
problematic due to their conceptual inconsistency. ‘The words are and remain for the music a
foreign extra of secondary value, as the effect of the tones is incomparably more powerful,
more infallible, and more rapid than that of the words’ (Schopenhauer, engl. transl. 1958,
448). Schopenhauer, of course, follows the hierarchy of the arts proposed by his own before,
and therefore regarded music as the most capable medium of expressing the inner contents:
...the musical art at once shows its power and superior capacity, since it gives
the most profound, ultimate, and secret information on the feeling expressed in the
words, or the action presented in the opera. It expresses their real and true nature, and
42
makes us acquainted with the innermost soul of the events and occurrences...
(Schopenhauer, engl. transl. 1958, p.448).
Accordingly, Schopenhauer suggests that it would be more appropriate to write the
text to already existing piece of music. However, he was acquainted with the usual and
practically convenient method of composing the music on already existed text or poem. He
finally concludes that music is able to express ‘every movement of the will, every feeling; but
through the addition of the words, we receive also their objects, the motives that give rise to
that feeling’ (Schopenhauer, engl. transl. 1958, p.449). It comes to this, that music does not
need the object to represent the content. Thus the classification of sound structure by itself as
musical phenomena was not the central idea; moreover, the role of physical sound as a
‘matter’ of music was neglected. Music does not have ‘matter’ in the terms of definable
phenomena representing the Ideas, expresses the ‘metaphysical to everything physical in the
world, the thing-in-itself to every phenomenon’ (Vol. I, p.262). Will as a noumenal mover of
phenomenal world is expressing itself in both phenomena and music, other arts are derived
secondary from phenomena, or are using its matter.
Contrary to Kantian conception of music as a play of sensations, music expresses
universal, pure form relating to the thing-in-itself and not to the phenomenon. According to
Green (1930, p.200),
...music must have deeper roots in human nature than the other arts, and that
whilst these are representations of external phenomena, themselves symbols of the real
essence of things, music is the representation of this essence itself, a parallel form,
therefore, of the World as our intellect perceives it.
Schopenhauer, then, understood music as the direct representation and objectification
of will:
Music, therefore, if regarded as an expression of the world, is in the highest
degree a universal language, which is related indeed to the universality of concepts,
much as they are related to the particular things... In this respect it resembles
geometrical figures and numbers, which are the universal forms of all possible objects
of experience and applicable to them all a priori, and yet are not abstract but
perceptible and thoroughly determined (The World as Will and Idea, translated by R.
B. Haldane and J. Kemp, 1883, vol. I, pp. 339-340.).
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The unity of will and multeity of its objectification induces that all phenomena have
identical ontogenesis. However, the organization of the pitches in the structure of musical
work does not suggest any ‘natural’ phenomenon.
‘We may regard the phenomenal world, or nature, and music as two different
expressions of the same thing [will], which is therefore itself the only medium of their
analogy, so that knowledge of it is demanded in order to understand that analogy.’
(Schopenhauer, The World as Will and Idea, translated by R. B. Haldane and J. Kemp,
1883, vol. I, pp. 339-342.)
This analogy is governed by musical proportion and melody, which reflects the ‘inner
spirit of the given phenomenon’. Melody has two dichotomical elements:
1. Rhythmical (quantitative): duration of the notes - vertical dimension.
2. Harmonious (qualitative): pitch and depth of the notes - horizontal dimension.
‘Rhythm is in time what symmetry is in space’ (Schopenhauer, 1958, p.453). This is
the only classification of phenomenal dimension of music in Schopenhauer’s text. Time and
space as the pure a priori forms which are prerequisites for perception, receiving object into
mind, might propose that rhythm and symmetry are the qualitative dimensions of these forms,
as well as a priori, while time and space are quantitative dimensions. Moreover, they might
be inextricably linked into rhythmic time and symmetrical space. The reason for this is that we
always are looking for proportions in time and space, for their organization. What is the
disadvantage of music for Kant - lack of definability in terms of concept and durability of
time; seems to be advantage for Schopenhauer - music is the essence, the pure form of the
will.
Music as the direct copy of the will has an influence on mind in qualitative different
way than phenomenal stimuli. The perceptual faculty does not contribute fundamentally to the
ontogenetical constitution of music. The musical reception suggests a process of recollection
of inner contents of the mind or memory rather than simple perception:
...that whoever gives himself up entirely to the impression of a symphony,
seems to see all the possible events of life and the world take place in himself, yet if
he reflects, he can find no likeness between the music and the things that passed
before his mind. For, as we have said, music is distinguished from all the other arts by
the fact that it is not a copy of the phenomenon, or, more accurately, the adequate
objectivity of will, but is the direct copy of the will itself, and therefore exhibits itself
as the metaphysical to everything physical in the world, and as the thing-in-itself to
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every phenomenon. (The World as Will and Idea, translated by R. B. Haldane and J.
Kemp, 1883, vol. I, p.340.)
Music ‘restores to us all the emotions of our inmost nature’, the listener under the
influence of musical stimuli is recollecting the primordial contents or a priori giveness of his
mind, which are, as Schopenhauer suggests, identical with the will. Music is also capable to
answer the most fundamental ontological questions more than ‘all the others [arts], since in a
language intelligible with absolute directness, yet not capable of translation into that of our
faculty of reason, it expresses the innermost nature of all life and existence.’ (Schopenhauer,
engl. transl. 1958, p.406) Schopenhauer ignored the phenomenal dimensions in music, its
‘sounding’ character, as well as its perceptional dimension, which later became the central
issue of phenomenology of music.
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Phenomenology and ontology of Music
While the last two chapters were devoted to the two contradictory but contiguous
philosophical conceptions of the metaphysical dimension of music, even not in terms of
autonomous philosophical sub-disciplines regarding ontology of music, the phenomenology
of music is implied discipline concerning with the two main spheres of interest: (i) the
examination of the way how is music perceptually constituted in a subject, emphasizing the
‘phenomenal dimension’ of music, and (ii) with the ontology of music occupied by
ontological status of musical piece.
Edmund Husserl (1859-1938), one o the most influential philosophers of the 20th
century, is regarded as foundator of philosophical phenomenology. Husserl’s interest in music
was restricted to the subjective temporal perception and inner constitution and temporal
organization of sensational data. However, as early as in the Antiquity and Middle Age, the
issue of mental organization of perceived data employed grammarians and philosophers to a
great extent in the discipline of ars memorandi. Aristotle, for example, wrote sole treatise On
Memory concerning the mental act of memory. According to Julius Victor, a fourth-century
grammarian, ‘memory is the firm mental grasp of things and words for the purpose of
invention’, (C. Julius Victor: ‘On Memory’ translated by Jan M. Ziolkowski 2004, p.297).
With reference to Carruthers and Ziolkowski (2004, p.3) ‘...as an art, memory was most
importantly associated in the Middle Ages with composition, not simply with retention.’
Memory was understood as cognitive faculty, which decomposes phenomena into simple
mental components. Husserl examination in phenomenology of music uses similar
methodology as that of the ars memorandi, although he tied up the rhetoric of modern
philosophers.
The phenomenology of music leads us back to the Kantian subjectivism - the
ontological dimension of the work is constituted in the inner action of subject. However,
Husserl refused the idea of exaggerative subjectivism, and did not believe that there are so
many worlds as they appear in individual subjective perceptions. He predicted ONE world
and ONE particular thing-in-itself but many appearances of it (Husserl, 1996, p.43). The
questions concerning with the metaphysics exceeds the borders of the world as a universe of
46
elementary facts (1996, p.31) He believed that the mathematical designation of pure nature
could be implemented through the methods of exactification the continuums, through
transformation of sensual causalities into mathematical causalities (1996, p.303), as it was
explained in the introduction to this writing. The methodology of natural sciences extracts the
truth from relativity of phenomena (1996, p.305), in consequence, the pure nature is
knowable. On the contrary, Kant refused the option of using pure notions of mind
transcendentally, so they could be applied exclusively to empirical experience (Kant, The
Critique of Pure Reason).
According to Husserl, the cognitional ability is invariably fixed to the consciousness
of object and therefore has an intentional nature. Consequently, the hearing cannot be
apprehended separately but with reference to the pitch. Any particular pitch depends on
quantitative specification, on mathematically definable and physically measurable parameters
such as the thickness of a string or its tenseness, and not on qualitative specification, such as
color or even sensational quality (1996, p.306). However, it appears that the ontology of
music differs from that of the pitch. The fundamental argument for this is that Husserl
distinguished between the pitch perceived and the hearing of the pitch. The antinomy between
sound and silence has a new, ontological dimension. Husserl accepted the existence of the
perceived pitch and sounding structures as objective, though this ‘materiality’ of the pitch and
sound structures is not apprehended as ‘music’.
According to Husserl, music has temporal and non-conceptual nature. Forasmuch as
music is constituted in the ‘inner subjective acts’, the subjective temporality became the
central issue of his examination.
It is indeed evident that the perception of a temporal object itself has
temporality, that perception of duration itself presupposes duration of perception, and
that perception of any temporal configuration whatsoever has its temporal form
(Husserl, Phenomenology, p.42, IN: Lippman, 1994, p.438)
The morphogeny of music and its real base lies in the acts of composition and
constitution of temporal sensational data into an object. This transformation is done through
cognitional and perceptual faculties. Husserl established the ontological contrast between
sound and music, between the temporal objectivity and materiality of sound structures and
inner temporal constitution. However, he did not provide further explanation concerning the
formal and conceptual sources of music.
47
Further investigation in phenomenology was concerned with the ontology of music.
Martin Heidegger (1889-1976), Husserl’s successor and critic, did not apprehend
phenomenology as an autonomous scientific discipline but as the method ‘how’ to examine.
However, his interest in the arts was restricted to the general question of its beauty, truth and
existence, music never stood in the main focus of his philosophical examination. Regarding
Husserl’s investigation in the terms of relation between sound materiality and its subjective
constitution, he considered that ‘the art work could not exist without the activity of the artist,
so the artist could not exist without the work of art’ (Stulberg, 1973, p. 257). This statement
reflects a bilateral dependency of objective status of a musical work and subjective status
representing by the artist.
Nelson Goodman and Roman Ingarden, were fully occupied themselves with
philosophical issue regarding ontological status of music. Roman Ingarden (1893-1970) dealt
also with related problems of performance, notation, and authenticity. For Husserl music,
according to its ontological status, was constituted through inner action of perception within a
subject, Ingarden posed quite different ontological point, regarding music not in general, but
music in particular, an actual musical work. The ontological status of a musical is inextricably
linked to the particular work. However, a new methodological problem arises: performance
versus ontological status of a work – the relation between an actual piece of music and its
multifarious performances.
...it is said that each time we hear that sonata [Chopin’s B Minor Sonata] in a
particular performance we hear the same sonata even though it is in every case a new
and somewhat different performance, since the performer and the conditions are
different (Ingarden, English transl.,1986, p.3).
Ingarden considered that ‘...musical work is not the same as its various
performances...’ (1986, p.9) Each performance of a certain musical work: (i) is a certain
individual occurrence (process) developing in time and placed in it univocally, (ii) is above all
an acoustic process, and (iii) is univocally fixed in space, both objectively and phenomenally
(1986, pp.10-11). Every musical work is than an object persisting in time (1986, p.15).
Ingarden, at last, was confronted with the ontological difference defined by sounding
and nonsounding qualities in music. Sounds (Ingarden uses a plural to underline particular
sounds in musical composition) are ‘spatially and temporarily individuated objects’; on the
contrary, a musical work is a ‘supraindividual and supratemporal structure’. The musical
48
work is a ‘multiphased structure in which the basic and elementary phenomena are sounding
or rustling (percussive) qualities’ (1986, p.83).
Ingarden describes the sound quality in music as the ‘chain of sound-constructs’.
However, these ‘sound-constructs’ do not ‘exhaust the work’s constitution, for there are also
various nonsounding qualities and constructs evidently superimposed upon the constructs’
(1986, pp.83-84). The totality of a musical work is constituted ‘when sound-constructs
combine with nonsounding ones’ (Ingarden, 1986, p.84).
The nonsounding elements are ‘not essential to all kinds of musical work just because
they do not appear in all of them’ (1986, p.88). Ingarden categorized the nonsounding
elements of a musical work as:
• Temporal or quasi-temporal structure of a musical work: closely connected with
the ‘properties of sound-constructs’. This temporal structure is also present in what
Ingarden calls ‘multiphased works of art’, such as literature, film, and drama.
• Movement: a ‘quite specific “motion” that accompanies the development of some
musical constructs’ (1986, p.90), e.g. the movement of individual voice in relation
to the others in Bach’s fugue.
• The forms of ‘specific musical constructs’, e.g. the shape and structure of melody
or chord.
• Emotional qualities: ‘They appear upon specific sound-constructs, both of a higher
and of a lower order…’ (1986, p.97).
• ‘Aesthetically valuable qualities’: they include all the nonsounding elements.
Music has an iconic, or representative functions if
a particular work does exercise the function of expressing the composer’s or
performer’s feelings, then the work evidently imparts information about something
other than itself, something which normally belongs to the real world (1986, pp.104-
105).
Ingarden apprehended a musical work as music itself, as the object of his examination.
However, he deviated from the point of his classification of nonsounding elements of a
musical work to the semantic aspects of a subjective perception of a musical work lying in
different methodological area. In the chapter ‘How does a musical work exist?’ of his The
Work of Music and the Problem of Its Identity, Ingarden specified the ontological status of a
49
musical work. Musical work originates in ‘specific, creative, psychosomatic acts by the
composer’. These acts culminate through notation or ‘immediate’ performance what Ingarden
characterized as ‘improvisation’. However, the musical work is not identical with the
‘arrangement of concrete sounds heard in specific performances’, it goes ‘outside the qualities
of concrete sounds’. A musical work is a ‘purely intentional object with its original source in
a specific real object and its ground of continued existence in a series of other real objects’
(1986, p.120).
Contrary to Ingarden, Nelson Goodman in his famous work Languages of Art (1976)
addressed himself to ontology in terms of authenticity and material delimitation of the arts. He
considered the ontological status of music as curious, because ‘music, unlike painting, there is
no such thing as a forgery of a known work’ (Goodman, 1976, p.112). He noted that
copies of the score may vary in accuracy, but all accurate copies, even if
forgeries of Haydn’s manuscript are equally genuine instances of the score.
Performances may vary in correctness and quality and even in ‚authenticity‘ of a more
esoteric kind; but all correct performances are equally genuine instances of the work.
In contrast, even the most exact copies of the Rembrandt painting are simply
imitations or forgeries, not new instances, of the work. Why this difference between
the two arts? (1976, p. 112-113)
On the basis of these and similar considerations, Goodman proposed nowadays
generally accepted categorization of the arts. The work of art might be:
• Autographic: distinction between original and forgery is significant; the most exact
duplication of work does not thereby count as genuine. Therefore, e.g. painting
belongs to the autographic art.
• Allographic: there is no distinction between the duplication of a work and its
original, e.g. music, literary arts.
The further division of the arts depends on the way of how work is done:
• One-stage: work is done by process of writing or painting (e.g. painting, writing)
• Two-stage: work is written but done though the performance (e.g. music, drama)
Therefore music is allographic and two-stage, painting is autographic and one-stage,
and literature is allographic and one-stage.
50
Contrary to the cosmology, phenomenology of music concerns exclusively with music
in particular, especially with musical work itself (Ingarden, Goodman) or with its perception –
particular sensual experience (Husserl). Phenomenology is focused to the ontological status of
musical work and subjective facets of its perception. The absorption in ontological status of
musical work, since the half of 20th century, may relate to augmentative historicism, early
music exploration, problems with definition of authenticity, and particularly to the ambition
of designation the concept of ‘Urtext’ as the clearest representation of composers’ intention.
Coessential for growing concern in ontology are questions of forgery, regarding artificial
work, and delimitation of copyright.
51
Conclusion
The antimony between silence and sound refers to the key issue of ontology of music:
is music explicitly a perceptual phenomenon or universal principle of primordial harmony?
Music as a sound-quality is apprehended perceptually, what can be verifiable empirically;
while music as silence-quality is a speculative, meta-perceptual music - this can be verified
through non-musical phenomena, e.g. planetary motions corresponding to musical
proportions. The basic problem of ontology, even of cosmology of music, is whether these
two opposite qualities are linked together in music, or if they can exist separately. Each
conception of cosmology, presented in this writing, is explaining the different way of linkage
between silence and sound qualities in music: Pythagoras suggests an ontogenetical unity of
all things; Plato believed that reality (sound) has a prototype existence in World-Soul
(silence); Boethius divided the phenomena of music in different categories in qualitative
order: Musica mundana (he believed that it is sonant), Musica humana (silent), and Musica
instrumentalis (sonant); and Kepler attempted to prove harmony of the world (silent)
empirically. On the contrary, Kant rejected knowability of metaphysical dimensions of music.
The Greek set of cosmological axioms could be summarized as follows (according to
Gentner & c., 1997):
• The Earth is at the center of the universe and is itself unmoving.
• The Earth is surrounded by physically real crystalline spheres, containing the heavenly
bodies, which revolve around the Earth.
• The heavenly bodies move in perfect circles at uniform velocity, as befits incorruptible
bodies. (Epicycles and eccentrically positioned circles were admitted into the system
to account for the observed motions.)
• All motion requires a mover. The outermost sphere, containing the fixed stars, is
moved by an ‘unmoved mover’, the Primum Mobile. Each sphere imparts motion to
the next one in; in the Aristotelian universe, there is no action-at-a-distance. In
52
addition, each sphere is controlled by its own spirit that mediates its motion. (The
heavenly bodies were known not to move in synchrony.)
• Celestial phenomena must be explained in entirely different terms from earthly
phenomena. Indeed, heavenly bodies and their spheres are made of different matter
altogether. They are composed not of the four terrestrial elements - earth, air, fire, and
water - but instead of a fifth element (the quintessence), crystalline aether (pure,
unalterable, transparent, and weightless). The further from Earth, the purer the sphere.
However, the exact scheme of the correspondence between the cosmos’ organization
and music has never been drawn. Thus we do not know whether each planet or sphere
represents particular tone or particular interval in dependence on the distance from the centre
(i.e. the Earth before Copernicus). This fact has two possible reasons: (i) the lack of
observational data and (ii) the view about the quality of cosmos. According to Greek tradition,
the universe was divided into two qualities: the ethernal spheres and spheres subjected to
permanent change. The usual distinction line was regarded to be the lunar sphere. The same
dimensions were attributed to human being, which took an inner journey accross the stages
identical with the spheres of the universe. Human being was a mirror of the universe; music
was an universal harmony linking the micro- and macro- dimensions together.
The role of deities in the cosmos was shifted in early Middle Ages. In 543, Justinian I,
Byzantine emperor, issued the decree of nine canons contra Origenem, the sixth canon
suppresses the belief that cosmos and celestial bodies are settled by rational beings (Grosse,
1994).
The first detailed proposal about celestial music was drawn by Johannes Kepler. His
interpretation of celestial music is more sophisticated in terms of modern science. He linked
together the Greek conception of musical numerology with empirics. This view on cosmos,
representing early empirics, was given by new observations and empirical data, and differs
from Greek view in these aspects:
• The centre of the universe is the Sun.
• The universe has a physical substance, and therefore is not divided into ethernal and
corruptive spheres.
• The planets move in elliptic orbits and their velocity is not constant.
• The mover of the solar system is the Sun.
53
• Celestial phenomena must be explained in the same terms as earthly phenomena. The
universe is made up from physical matter.
It is possible to draw parallels among various conceptions of musical cosmology as
well as with contemporary theories. Boethius wrote about the cycles and elements of nature as
a part of Musica Mundana. The same assumption that the variability of nature has its rules
subjected to the proportions of Musica Mundana can be found in Kepler: ‘...soul which we
call sublunary Nature, which controls meteorological phenomena according to the rules of
proportions which occur in the radiations of the stars.’ (Harmonices Mundi Lber III, Source:
Godwin, 1986, p.150). In spite of empirical data, Kepler still believed in astrological
influence on earthly phenomena and human being in terms of harmonic proportions identical
with those of music and carried by species immateriata.
Kepler also made contributions in the field of optics and developed a system of
infinitesimals in mathematics, which was a forerunner of calculus. The superparticular and
reciprocal musical ratios are, in fact, the two infinitesimals having identical limit: number one
- the mathematical basis for universe. Ratios derived from Pythagorean tetractys are
equivalent to the oscillating patterns of sub-elementary particles - so called strings - in string
field theory. The pattern of oscillation based on number or numerical ratio is believed to be
the key feature of the matter. The fact, that this oscillations are supposed to exist in more than
three-dimensional spaces substitute the former myth about metaphysical dimensions. In a
metaphorical sense, the string represents an equilibrial principle that penetrates the whole
cosmos. Once a string is plucked a many of dynamic qualities emerge from quiescent
condition. This is just a birth of sound from the realm of silence.
The early empirics of the end of 16th and beginning of 17th century brought in both
cognitive optimism and ontological skepticism. One might ask why such progressive scientist
as Galileo Galilei took recourse to relationship of simple craftsmen (Heer, 1965). The old
belief of epistemological unity between the universe - an objective world, and human being -
individual subject, was irretrievably lost. Modern scientists turned away from an ‘external
authorities’ and became to understand that experience has a key epistemological importance
dividing the reality into subject and object. This may be classified as ‘ontological schism’.
Kantian approach represents an antipole to the classical cosmology; he refused the
cosmology as an objective authority given to us and hyposthased the epistemological role of
subjectivity. For Kepler, the same rules were applied to the universe and to a man, but Kant
54
defined methodological difference between the universe and subject, between the thing-in-
itself and phenomenon - a thing as it is given to us. On the contrary, Schopenhauer turned
back to the ‘modern cosmology’, when he had introduced the concept of Will objectifying
itself in the universe. Will, analogous to Pythagorean tetractys, is an epigenetic source of all
phenomena.
Sound concepts and sounding structures are not considered to be music in itself
(Husserl, Ingarden). Sound does not exist in ontological terms; it only lasts for particular
period of time as a phenomenon (Kant). Sound is a ‘Heidegger’s phenomenon’ that hints at
something what does not represent by itself. Thus music is reflecting through something what
appears. The existence of sound is nothing but appearance by itself. According to Ingarden
and Husserl, music emerges through interaction between object (sound-concepts) and
subjective perception of this object.
The ontology of music does not mean that music exists in ‘ontological pre-shape’,
because our notion of perceptual music is simply not possible to adopt for ontological status
of music - thing-in-itself, but in epigenetic forms determining subjective perception (Wallin,
1991) there is a real basic - a potential for perceptual music - resting in the state of silence.
According to (i) cosmology of music, these potential epigenetic forms are in basic proportions
of numeric ratios; (ii) Kant, in a priori givenness of mind and (?) body; and (iii)
Schopenhauer, in Will and all its modifications. The primordial pre-shaping of perceptual
physiological options predetermines how music is perceived and predetermines also the
structure of music itself. The theory of ‚Ursatz‘ in Schenkerian analysis suggests implicitly
that music is believed or presupposed to exist in a couple of modifications of the primeval
stable model with many morphodynamic possibilities for further development.
55
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